The main structure of a puppet is made entirely of 1/2" foam. I have been strictly working with upholstery foam because of its availability. It is far more dense than its professional brother: reticulated foam aka filter foam but the construction methods are the same. The only downside is that upholstery foam is a little less forgiving, so take your time when gluing the pieces together.
Start by tracing your pattern on the foam. Be sure to mirror your patterns for both sides of the head.
Using an insanely sharp razor, cut your patterns out. Take special care that your knife is perpendicular to the foam, an out-of-square cut can lead to wobbly puppets.
Once every piece is cut, use a scrap chunk of foam as a stippling applicator for your contact cement. I use Weldwood contact cement from the hardware store, but most pros use Barge cement, both work great. Apply glue conservatively to both surfaces that you plan to stick together. Contact cement only adheres to itself and only once it has dried to the touch, so let your glued pieces sit for a good ten minutes or so.
Now that your glue has dried a bit, start gluing the darts together on each piece, being sure to line everything up nice and even while allowing the foam to begin to curve to shape. Next, stick all the pieces together and you have a naked puppet skull!